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The movement of a solid in an incompressible perfect fluid as a geodesic flow

Abstract : The motion of a rigid body immersed in an incompressible perfect fluid which occupies a three-dimensional bounded domain have been recently studied under its PDE formulation. In particular classical solutions have been shown to exist locally in time. In this note, following the celebrated result of Arnold concerning the case of a perfect incompressible fluid alone, we prove that these classical solutions are the geodesics of a Riemannian manifold of infinite dimension, in the sense that they are the critical points of an action, which is the integral over time of the total kinetic energy of the fluid-rigid body system.
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https://hal.archives-ouvertes.fr/hal-00564114
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Submitted on : Tuesday, February 8, 2011 - 9:35:53 AM
Last modification on : Friday, April 29, 2022 - 1:56:08 PM

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Olivier Glass, Franck Sueur. The movement of a solid in an incompressible perfect fluid as a geodesic flow. Proceedings of the American Mathematical Society, American Mathematical Society, 2012, 140, pp.2155-2168. ⟨10.1090/S0002-9939-2011-11219-X⟩. ⟨hal-00564114⟩

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